Ce matin, Paul cherchait sa calculatrice pendant que la professeure préparait un questionnaire.

Because the sentence describes two ongoing actions in the past:

• Paul was looking for his calculator
• the teacher was preparing a quiz

In French, the imparfait is commonly used for:

• background description
• repeated or habitual actions
• actions in progress in the past

Here, both actions were happening at the same time, so the imparfait fits well.

If you used the passé composé, it would sound more like completed events:

• Paul a cherché sa calculatrice pendant que la professeure a préparé un questionnaire.

That version is grammatically possible in some contexts, but it does not give the same “ongoing background” feeling.

Pendant que means while.

It connects two actions that happen at the same time:

• Paul cherchait sa calculatrice
• la professeure préparait un questionnaire

So:

• Paul cherchait sa calculatrice pendant que la professeure préparait un questionnaire = Paul was looking for his calculator while the teacher was preparing a quiz.

It is a very common way to link simultaneous past actions.

Because in French, chercher takes a direct object.

So French says:

• chercher quelque chose
• chercher sa calculatrice

English uses look for, which includes for, but French does not use a preposition here.

So:

• I’m looking for my keys → Je cherche mes clés
• Paul was looking for his calculator → Paul cherchait sa calculatrice

This is a very common difference between French and English.

In French, the possessive adjective agrees with the thing possessed, not with the owner.

Here:

• calculatrice is feminine singular
• so the possessive must also be feminine singular: sa

That is true even if the owner is a man.

So:

• Paul cherche sa calculatrice = Paul is looking for his calculator
• Marie cherche sa calculatrice = Marie is looking for her calculator

In both cases, it is sa because calculatrice is feminine.

Ce matin means this morning.

French often puts a time expression at the beginning of the sentence to set the scene:

• Ce matin, ...
• Hier, ...
• À midi, ...

This is very natural and common. It helps give context before the main action.

You could also place it later:

• Paul cherchait sa calculatrice ce matin pendant que la professeure préparait un questionnaire.

But the original version sounds smoother because it introduces the time first.

The comma is used because Ce matin is an introductory time expression.

In English, we often do the same:

• This morning, Paul was looking for his calculator...

In French, the comma after a short introductory phrase is common, especially in clear written style. Sometimes people omit it in informal writing, but here it is perfectly normal.

La professeure is a feminine form meaning the female teacher/professor.

Modern French increasingly uses feminine job titles for women:

• un professeur / une professeure
• un acteur / une actrice
• un directeur / une directrice

You may also see:

• la prof
• sometimes even le professeur for a woman in older or more traditional usage

But la professeure is clear and natural in contemporary French.

Because the sentence introduces it as a questionnaire, not a specific one already known to the listener.

French uses:

• un / une for something non-specific or newly introduced
• le / la for something specific or already identified

So:

• préparait un questionnaire = was preparing a questionnaire
• préparait le questionnaire = was preparing the questionnaire

The original sentence does not suggest that the listener already knows which questionnaire it is, so un is the natural choice.

Yes, you could say:

• Ce matin, Paul était en train de chercher sa calculatrice pendant que la professeure préparait un questionnaire.

This means roughly:

• Paul was in the middle of looking for his calculator...

Both are correct, but they are slightly different in tone:

• cherchait = simple, natural imperfect; very common
• était en train de chercher = more explicit emphasis on the action being in progress

In many cases, French prefers the simpler imparfait unless there is a reason to stress the ongoing nature.

Because Paul is a proper noun, and proper nouns in French usually do not take an article.

So:

• Paul cherchait...
• Marie parlait...
• Jean arrivait...

That is just like English:

• Paul was looking...

There are some special cases in French where names can appear with articles, but not in a normal sentence like this one.

Not necessarily. Ce matin literally means this morning, but its exact time reference depends on the context.

For example:

• If it is still morning, ce matin may refer to earlier today.
• If the speaker is talking later in the day, it still means this morning in relation to today.

So it can appear with a past tense very naturally:

• Ce matin, Paul cherchait sa calculatrice...

That simply means the action happened this morning, and the verb tense tells you it is being described as a past event.

Yes. You could say:

• Ce matin, la professeure préparait un questionnaire pendant que Paul cherchait sa calculatrice.

That is also correct.

The difference is mainly one of focus:

• original sentence: attention first on Paul
• reversed sentence: attention first on the teacher

French is flexible here, as long as the relationship between the two actions remains clear.